Average Error: 1.6 → 1.7
Time: 34.2s
Precision: 64
Internal Precision: 576
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|(\left(x + 4\right) \cdot \left(\frac{1}{y}\right) + \left(-\frac{x}{y} \cdot z\right))_*\right|\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 1.6

    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
  2. Using strategy rm

  3. Applied div-inv1.7

    \[\leadsto \left|\color{blue}{\left(x + 4\right) \cdot \frac{1}{y}} - \frac{x}{y} \cdot z\right|\]

  4. Applied fma-neg1.7

    \[\leadsto \left|\color{blue}{(\left(x + 4\right) \cdot \left(\frac{1}{y}\right) + \left(-\frac{x}{y} \cdot z\right))_*}\right|\]

Runtime

Time bar (total: 34.2s)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))